C

U

SB

Given:

Prove:

Statement Reason

1.𝑈𝐵𝑖𝑠𝑎𝑚𝑒𝑑𝑖𝑎𝑛𝑡𝑜𝐶𝑆 1. Given

2.𝑈𝐶≅𝑈𝑆 2. Given

3.𝐵𝑖𝑠 h𝑡 𝑒𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝐶𝑆 3. A median extends from the vertex of a triangle to the midpoint of the opposite side

4.𝐶𝐵≅𝑆𝐵 4. A midpoint divides a segment into two congruent parts

5.𝑈𝐵≅𝑈𝐵 5. Reflexive Postulate

6. ∆𝐶𝑈𝐵 ≅ ∆𝑆𝑈𝐵 6. SSS SSS

Statement Reason

L

K

RS

A E

Given:

Prove:

1.𝐿𝐴≅𝑅𝐸 1. Given

2. 𝐴𝐾 ≅ 𝐸𝐾 2. Given

3.𝑆𝑖𝑠 h𝑡 𝑒𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝐿𝑅 3. Given

4.𝐿𝐴+𝐴𝐾 ≅𝑅𝐸+𝐸𝐾 4. Addition Postulate

5. Partition Postulate

6.𝐿𝐾 ≅𝑅𝐾 6. Substitution Postulate

7.𝐿𝑆≅ 𝑆𝑅 7. A midpoint divides a segment into two congruent parts

8.𝑆𝐾 ≅ 𝑆𝐾 8. Reflexive Postulate

9. ∆ 𝐿𝐾𝑆 ≅ ∆𝑅𝐾𝑆 9. SSS SSS

Proving Triangles Congruent

Mixed Problems

Statement Reason

1. Given

2. Given

Pg. 7 #1

21 2.

pairlinear a form and 2 pairlinear a form and 1 .4

GDCFBC

4. Two adjacent angles that

form a straight line are a linear pair

DGCBFC ΔΔ .8 ASAASA .8

BD C ofmidpoint theis 1.

5. Linear pairs are supplementaryarysupplement are and 2

arysupplement are and 1 .5GDCFBC

.6 GDCFBC 6. Supplements of congruent angles are congruent

CDB C .3 3. A midpoint divides a segment into two congruent parts

4 3 .7 7. Vertical angles are congruent

Statement Reason

1. Given

Pg. 7 #2

1. ADFA

anglesright are and .5 DA 5. Perpendicular segments

form right angles

DCEABF ΔΔ .11 SASSAS .11

6. All right angles are congruentDA 6.

CBCB 7.

2. Given 2. ADED 3. Given 3. DEAF 4. Given 4. DBAC

7. Reflexive postulate

CBDBCBAC .8 8. Subtraction Postulate

9. Partition Postulate

CDAB 10. 10. Substitution Postulate

CDCBDBABCBAC

.9

Statement Reason

1. Given

2. Given

Pg. 7 #3

CBAD 1.

CBAADC ΔΔ .4 SASSAS .4

ACAC .3 3. Reflexive postulate

21 2.

Statement Reason

RSTP base median to a is 2. 2. Given

Pg. 7 #4

RSP ofmidpoint theis 3.

SPRP 4.

3. A median extends from a vertex to a midpoint of the opposite side of a triangle.

4. A midpoint divides a segment into two congruent parts

1. Given

TPTP 5. 5. Reflexive postulate

STPRTP ΔΔ .6 SSSSSS .6

STRTRST

with triangleIsosceles 1.

Statement Reason

ABCD median to a is 1.

3. Given

Pg. 7 #5

CFCE 3.

1. Given

CDCD 9. 9. Reflexive postulate

BDCADC ΔΔ .10 SSSSSS .10

FBEA 2. 2. Given

FBCFEACE .6 6. Addition Postulate

7. Partition Postulate

CBCA 8. 8. Substitution Postulate

CBFBCF

CAEACE

.7

ABD ofmidpoint theis 4.

DBAD 5.

4. A median extends from a vertex to a midpoint of the opposite side of a triangle.

5. A midpoint divides a segment into two congruent parts

Statement Reason

FBCACB 2. 2. Given

Pg. 7 #7

EBCE 5.

CDFB 6.

5. A midpoint divides a segment into two congruent parts

BCE ofmidpoint theis 1. 1. Given

BFECDE ΔΔ .7 SASSAS .7

ADFB 4. 4. Given

CDAD 3. 3. Given

6. Substitution postulate

Statement Reason

QMRM 2. 2. Given

Pg. 7 #8

anglesright are and 5. SMPSML

SMPSML 6.

5. Perpendicular segments form right angles

LPMS

ofbisector lar perpendicu theis 1. 1. Given

QPMRLM ΔΔ .10 SASSAS .10

MPLM 4. 4. A segment bisector divides a segment into two congruent parts

ba 3. 3. Given

6. All right angles are congruent

bSMPaSML .7 7. Subtraction Postulate

8. Partition Postulate

QMPRML 9. 9. Substitution Postulate

QMPbSMPRMLaSML

.8